ring_theory.algebra_tower | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

94825b2b

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

93287238

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
 import Algebra.Algebra.Tower
-import Algebra.Invertible
+import Algebra.Invertible.Defs
 import Algebra.Module.BigOperators
 import LinearAlgebra.Basis

93287238

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -132,14 +132,14 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     (hb : LinearIndependent R b) (hc : LinearIndependent S c) :
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 :=
   by
-  rw [linearIndependent_iff'] at hb hc ; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
+  rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
   · have h1 : ∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2 = 0 := by rw [← hsg];
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>
             show g p • b p.1 • c p.2 = 0 by rw [hg p hp, zero_smul]).symm
-    rw [Finset.sum_product_right] at h1 
-    simp_rw [← smul_assoc, ← Finset.sum_smul] at h1 
+    rw [Finset.sum_product_right] at h1
+    simp_rw [← smul_assoc, ← Finset.sum_smul] at h1
     exact hb _ _ (hc _ _ h1 k (Finset.mem_image_of_mem _ hik)) i (Finset.mem_image_of_mem _ hik)
   exact hg _ hik
 #align linear_independent_smul linearIndependent_smul

93287238

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.Algebra.Algebra.Tower
-import Mathbin.Algebra.Invertible
-import Mathbin.Algebra.Module.BigOperators
-import Mathbin.LinearAlgebra.Basis
+import Algebra.Algebra.Tower
+import Algebra.Invertible
+import Algebra.Module.BigOperators
+import LinearAlgebra.Basis
 
 #align_import ring_theory.algebra_tower from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"

93287238

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.algebra_tower
-! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Tower
 import Mathbin.Algebra.Invertible
 import Mathbin.Algebra.Module.BigOperators
 import Mathbin.LinearAlgebra.Basis
 
+#align_import ring_theory.algebra_tower from "leanprover-community/mathlib"@"932872382355f00112641d305ba0619305dc8642"
+
 /-!
 # Towers of algebras

93287238

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -52,6 +52,7 @@ variable [IsScalarTower R S A] [IsScalarTower R S B]
 
 variable (R S A B)
 
+#print IsScalarTower.Invertible.algebraTower /-
 /-- Suppose that `R -> S -> A` is a tower of algebras.
 If an element `r : R` is invertible in `S`, then it is invertible in `A`. -/
 def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
@@ -59,13 +60,16 @@ def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
   Invertible.copy (Invertible.map (algebraMap S A) (algebraMap R S r)) (algebraMap R A r)
     (IsScalarTower.algebraMap_apply R S A r)
 #align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTower
+-/
 
+#print IsScalarTower.invertibleAlgebraCoeNat /-
 /-- A natural number that is invertible when coerced to `R` is also invertible
 when coerced to any `R`-algebra. -/
 def invertibleAlgebraCoeNat (n : ℕ) [inv : Invertible (n : R)] : Invertible (n : A) :=
   haveI : Invertible (algebraMap ℕ R n) := inv
   invertible.algebra_tower ℕ R A n
 #align is_scalar_tower.invertible_algebra_coe_nat IsScalarTower.invertibleAlgebraCoeNat
+-/
 
 end Semiring
 
@@ -87,21 +91,27 @@ variable [Algebra R A] [Module A M] [Module R M] [IsScalarTower R A M]
 
 variable (b : Basis ι R M) (h : Function.Bijective (algebraMap R A))
 
+#print Basis.algebraMapCoeffs /-
 /-- If `R` and `A` have a bijective `algebra_map R A` and act identically on `M`,
 then a basis for `M` as `R`-module is also a basis for `M` as `R'`-module. -/
 @[simps]
 noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
   b.mapCoeffs (RingEquiv.ofBijective _ h) fun c x => by simp
 #align basis.algebra_map_coeffs Basis.algebraMapCoeffs
+-/
 
+#print Basis.algebraMapCoeffs_apply /-
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
 #align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_apply
+-/
 
+#print Basis.coe_algebraMapCoeffs /-
 @[simp]
 theorem Basis.coe_algebraMapCoeffs : (b.algebraMapCoeffs A h : ι → M) = b :=
   b.coe_mapCoeffs _ _
 #align basis.coe_algebra_map_coeffs Basis.coe_algebraMapCoeffs
+-/
 
 end AlgebraMapCoeffs
 
@@ -151,15 +161,19 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 #align basis.smul Basis.smul
 -/
 
+#print Basis.smul_repr /-
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
     (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]
 #align basis.smul_repr Basis.smul_repr
+-/
 
+#print Basis.smul_repr_mk /-
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)
     (x i j) : (b.smul c).repr x (i, j) = b.repr (c.repr x j) i :=
   b.smul_repr c x (i, j)
 #align basis.smul_repr_mk Basis.smul_repr_mk
+-/
 
 #print Basis.smul_apply /-
 @[simp]
@@ -185,11 +199,13 @@ variable {R S}
 
 variable [CommRing R] [Ring S] [Algebra R S]
 
+#print Basis.algebraMap_injective /-
 theorem Basis.algebraMap_injective {ι : Type _} [NoZeroDivisors R] [Nontrivial S]
     (b : Basis ι R S) : Function.Injective (algebraMap R S) :=
   have : NoZeroSMulDivisors R S := b.NoZeroSMulDivisors
   NoZeroSMulDivisors.algebraMap_injective R S
 #align basis.algebra_map_injective Basis.algebraMap_injective
+-/
 
 end Ring

93287238

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -127,8 +127,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
   by
   rw [linearIndependent_iff'] at hb hc ; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
-  · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
-      rw [← hsg];
+  · have h1 : ∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2 = 0 := by rw [← hsg];
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>
             show g p • b p.1 • c p.2 = 0 by rw [hg p hp, zero_smul]).symm

93287238

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -125,15 +125,15 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     (hb : LinearIndependent R b) (hc : LinearIndependent S c) :
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 :=
   by
-  rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
+  rw [linearIndependent_iff'] at hb hc ; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
   · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
       rw [← hsg];
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>
             show g p • b p.1 • c p.2 = 0 by rw [hg p hp, zero_smul]).symm
-    rw [Finset.sum_product_right] at h1
-    simp_rw [← smul_assoc, ← Finset.sum_smul] at h1
+    rw [Finset.sum_product_right] at h1 
+    simp_rw [← smul_assoc, ← Finset.sum_smul] at h1 
     exact hb _ _ (hc _ _ h1 k (Finset.mem_image_of_mem _ hik)) i (Finset.mem_image_of_mem _ hik)
   exact hg _ hik
 #align linear_independent_smul linearIndependent_smul
@@ -219,7 +219,7 @@ variable {B}
 
 #print algHomEquivSigma /-
 /-- `alg_hom`s from the top of a tower are equivalent to a pair of `alg_hom`s. -/
-def algHomEquivSigma : (C →ₐ[A] D) ≃ Σf : B →ₐ[A] D, @AlgHom B C D _ _ _ _ f.toRingHom.toAlgebra
+def algHomEquivSigma : (C →ₐ[A] D) ≃ Σ f : B →ₐ[A] D, @AlgHom B C D _ _ _ _ f.toRingHom.toAlgebra
     where
   toFun f := ⟨f.restrictDomain B, f.extendScalars B⟩
   invFun fg :=

93287238

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -34,7 +34,7 @@ base rings to be a field, so we also generalize the lemma to rings in this file.
 -/
 
 
-open Pointwise
+open scoped Pointwise
 
 universe u v w u₁
 
@@ -109,7 +109,7 @@ section Semiring
 
 open Finsupp
 
-open BigOperators Classical
+open scoped BigOperators Classical
 
 universe v₁ w₁

93287238

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -52,9 +52,6 @@ variable [IsScalarTower R S A] [IsScalarTower R S B]
 
 variable (R S A B)
 
-/- warning: is_scalar_tower.invertible.algebra_tower -> IsScalarTower.Invertible.algebraTower is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTowerₓ'. -/
 /-- Suppose that `R -> S -> A` is a tower of algebras.
 If an element `r : R` is invertible in `S`, then it is invertible in `A`. -/
 def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
@@ -63,12 +60,6 @@ def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
     (IsScalarTower.algebraMap_apply R S A r)
 #align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTower
 
-/- warning: is_scalar_tower.invertible_algebra_coe_nat -> IsScalarTower.invertibleAlgebraCoeNat is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_3 : Semiring.{u2} A] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_3] (n : Nat) [inv : Invertible.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)], Invertible.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat A (HasLiftT.mk.{1, succ u2} Nat A (CoeTCₓ.coe.{1, succ u2} Nat A (Nat.castCoe.{u2} A (AddMonoidWithOne.toNatCast.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))))) n)
-but is expected to have type
-  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_3 : Semiring.{u2} A] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_3] (n : Nat) [inv : Invertible.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)], Invertible.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Semiring.toOne.{u2} A _inst_3) (Nat.cast.{u2} A (Semiring.toNatCast.{u2} A _inst_3) n)
-Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible_algebra_coe_nat IsScalarTower.invertibleAlgebraCoeNatₓ'. -/
 /-- A natural number that is invertible when coerced to `R` is also invertible
 when coerced to any `R`-algebra. -/
 def invertibleAlgebraCoeNat (n : ℕ) [inv : Invertible (n : R)] : Invertible (n : A) :=
@@ -96,12 +87,6 @@ variable [Algebra R A] [Module A M] [Module R M] [IsScalarTower R A M]
 
 variable (b : Basis ι R M) (h : Function.Bijective (algebraMap R A))
 
-/- warning: basis.algebra_map_coeffs -> Basis.algebraMapCoeffs is a dubious translation:
-lean 3 declaration is
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 /-- If `R` and `A` have a bijective `algebra_map R A` and act identically on `M`,
 then a basis for `M` as `R`-module is also a basis for `M` as `R'`-module. -/
 @[simps]
@@ -109,19 +94,10 @@ noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
   b.mapCoeffs (RingEquiv.ofBijective _ h) fun c x => by simp
 #align basis.algebra_map_coeffs Basis.algebraMapCoeffs
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_applyₓ'. -/
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
 #align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_apply
 
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-Case conversion may be inaccurate. Consider using '#align basis.coe_algebra_map_coeffs Basis.coe_algebraMapCoeffsₓ'. -/
 @[simp]
 theorem Basis.coe_algebraMapCoeffs : (b.algebraMapCoeffs A h : ι → M) = b :=
   b.coe_mapCoeffs _ _
@@ -176,17 +152,11 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 #align basis.smul Basis.smul
 -/
 
-/- warning: basis.smul_repr -> Basis.smul_repr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.smul_repr Basis.smul_reprₓ'. -/
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
     (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]
 #align basis.smul_repr Basis.smul_repr
 
-/- warning: basis.smul_repr_mk -> Basis.smul_repr_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.smul_repr_mk Basis.smul_repr_mkₓ'. -/
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)
     (x i j) : (b.smul c).repr x (i, j) = b.repr (c.repr x j) i :=
   b.smul_repr c x (i, j)
@@ -216,12 +186,6 @@ variable {R S}
 
 variable [CommRing R] [Ring S] [Algebra R S]
 
-/- warning: basis.algebra_map_injective -> Basis.algebraMap_injective is a dubious translation:
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 theorem Basis.algebraMap_injective {ι : Type _} [NoZeroDivisors R] [Nontrivial S]
     (b : Basis ι R S) : Function.Injective (algebraMap R S) :=
   have : NoZeroSMulDivisors R S := b.NoZeroSMulDivisors

93287238

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -151,9 +151,8 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
   by
   rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
-  · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 :=
-      by
-      rw [← hsg]
+  · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
+      rw [← hsg];
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>
             show g p • b p.1 • c p.2 = 0 by rw [hg p hp, zero_smul]).symm
@@ -262,16 +261,10 @@ def algHomEquivSigma : (C →ₐ[A] D) ≃ Σf : B →ₐ[A] D, @AlgHom B C D _
   invFun fg :=
     let alg := fg.1.toRingHom.toAlgebra
     fg.2.restrictScalars A
-  left_inv f := by
-    dsimp only
-    ext
-    rfl
+  left_inv f := by dsimp only; ext; rfl
   right_inv := by
     rintro ⟨⟨f, _, _, _, _, _⟩, g, _, _, _, _, hg⟩
-    obtain rfl : f = fun x => g (algebraMap B C x) :=
-      by
-      ext
-      exact (hg x).symm
+    obtain rfl : f = fun x => g (algebraMap B C x) := by ext; exact (hg x).symm
     rfl
 #align alg_hom_equiv_sigma algHomEquivSigma
 -/

93287238

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -53,10 +53,7 @@ variable [IsScalarTower R S A] [IsScalarTower R S B]
 variable (R S A B)
 
 /- warning: is_scalar_tower.invertible.algebra_tower -> IsScalarTower.Invertible.algebraTower is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTowerₓ'. -/
 /-- Suppose that `R -> S -> A` is a tower of algebras.
 If an element `r : R` is invertible in `S`, then it is invertible in `A`. -/
@@ -113,10 +110,7 @@ noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
 #align basis.algebra_map_coeffs Basis.algebraMapCoeffs
 
 /- warning: basis.algebra_map_coeffs_apply -> Basis.algebraMapCoeffs_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_applyₓ'. -/
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
@@ -184,10 +178,7 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 -/
 
 /- warning: basis.smul_repr -> Basis.smul_repr is a dubious translation:
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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, 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(Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.smul_repr Basis.smul_reprₓ'. -/
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
@@ -195,10 +186,7 @@ theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c
 #align basis.smul_repr Basis.smul_repr
 
 /- warning: basis.smul_repr_mk -> Basis.smul_repr_mk is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, 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(AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} R (coeFn.{max (succ (max u4 u5)) (succ u1), max (succ (max u4 u5)) (succ u1)} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R 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(AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} ((fun 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(Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) j)) i)
+<too large>
 Case conversion may be inaccurate. Consider using '#align basis.smul_repr_mk Basis.smul_repr_mkₓ'. -/
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)
     (x i j) : (b.smul c).repr x (i, j) = b.repr (c.repr x j) i :=

93287238

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -187,7 +187,7 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (ij : Prod.{u4, u5} ι ι'), Eq.{succ u1} R (coeFn.{max (succ (max u4 u5)) (succ u1), max (succ (max u4 u5)) (succ u1)} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => (Prod.{u4, u5} ι ι') -> R) (Finsupp.coeFun.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u3) (succ (max (max u4 u5) u1)), max (succ u3) (succ (max (max u4 u5) u1))} (LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => A -> (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max (max u4 u5) u1} R R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{max u4 u5, u1, u3} (Prod.{u4, u5} ι ι') R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 (Basis.smul.{u1, u2, u3, u4, u5} R S A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 ι ι' b c)) x) ij) (coeFn.{max (succ u4) (succ u1), max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) 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(RingHomInvPair.ids.{u2} S _inst_2)) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (ij : Prod.{u4, u5} ι ι'), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) ij) (FunLike.coe.{max (succ (max u4 u5)) (succ u1), succ (max u4 u5), succ u1} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.{u4, u5} ι ι') (fun (_x : Prod.{u4, u5} ι ι') => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) _x) (Finsupp.funLike.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (max (succ u1) (succ u4)) (succ u3)) (succ u5), succ u3, max (max (succ u1) (succ u4)) (succ u5)} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max (max u1 u4) u3) u5, u1, u3, max (max u1 u4) u5} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u1, u3} R A 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u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) b) (FunLike.coe.{max 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_inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (ij : Prod.{u4, u5} ι ι'), Eq.{succ u1} ((fun 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u3, max (max u1 u4) u5, max (max 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u4, max (max u1 u2) u4} R R S (Finsupp.{u4, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.{u1, u1, u2, max u1 u4} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R 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(CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u4} R R S (Finsupp.{u4, u1} ι R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) b) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι') => S) _x) (Finsupp.funLike.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u5), succ u3, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
 Case conversion may be inaccurate. Consider using '#align basis.smul_repr Basis.smul_reprₓ'. -/
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
@@ -198,7 +198,7 @@ theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} R (coeFn.{max (succ (max u4 u5)) (succ u1), max (succ (max u4 u5)) (succ u1)} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => (Prod.{u4, u5} ι ι') -> R) (Finsupp.coeFun.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u3) (succ (max (max u4 u5) u1)), max (succ u3) (succ (max (max u4 u5) u1))} (LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) => A -> (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (LinearEquiv.hasCoeToFun.{u1, u1, u3, max (max u4 u5) u1} R R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{max u4 u5, u1, u3} (Prod.{u4, u5} ι ι') R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6 (Basis.smul.{u1, u2, u3, u4, u5} R S A _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 ι ι' b c)) x) (Prod.mk.{u4, u5} ι ι' i j)) (coeFn.{max (succ u4) (succ u1), max (succ u4) (succ u1)} (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => ι -> R) (Finsupp.coeFun.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u2) (succ (max u4 u1)), max (succ u2) (succ (max u4 u1))} (LinearEquiv.{u1, u1, u2, max u4 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) S (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u2, max u4 u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) S (Finsupp.{u4, u1} ι R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u4, u1} ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Basis.repr.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) b) (coeFn.{max (succ u5) (succ u2), max (succ u5) (succ u2)} (Finsupp.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (fun (_x : Finsupp.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) => ι' -> S) (Finsupp.coeFun.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S 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(Semiring.toModule.{u2} S _inst_2))) (fun (_x : LinearEquiv.{u2, u2, u3, max u5 u2} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) => A -> (Finsupp.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (LinearEquiv.hasCoeToFun.{u2, u2, u3, max u5 u2} S S A (Finsupp.{u5, u2} ι' S (MulZeroClass.toHasZero.{u2} S (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) j)) i)
 but is expected to have type
-  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) (Prod.mk.{u4, u5} ι ι' i j)) (FunLike.coe.{max (succ (max u4 u5)) (succ u1), succ (max u4 u5), succ u1} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.{u4, u5} ι ι') (fun (_x : Prod.{u4, u5} ι ι') => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) _x) (Finsupp.funLike.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (max (succ u1) (succ u4)) (succ u3)) (succ u5), succ u3, max (max (succ u1) (succ u4)) (succ u5)} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max (max u1 u4) u3) u5, u1, u3, max (max u1 u4) u5} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max (max u1 u4) u3) u5, u1, u3, max (max u1 u4) u5} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (Module.toDistribMulAction.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R 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_inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) j)) i)
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) (Prod.mk.{u4, u5} ι ι' i j)) (FunLike.coe.{max (succ (max u4 u5)) (succ u1), succ (max u4 u5), succ u1} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Prod.{u4, u5} ι ι') (fun (_x : Prod.{u4, u5} ι ι') => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Prod.{u4, u5} ι ι') => R) _x) (Finsupp.funLike.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (FunLike.coe.{max (max (max (succ u1) (succ u4)) (succ u3)) (succ u5), succ u3, max (max (succ u1) (succ u4)) (succ u5)} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _x) (SMulHomClass.toFunLike.{max (max (max u1 u4) u3) u5, u1, u3, max (max u1 u4) u5} (LinearEquiv.{u1, u1, u3, max u1 u4 u5} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) R A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u1, u3} R A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u1, u3} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (Module.toDistribMulAction.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)))) (SMulZeroClass.toSMul.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (AddCommMonoid.toAddMonoid.{max (max u1 u4) u5} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max (max u1 u4) u5} R (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) 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u2} R S _inst_1 _inst_2 _inst_4) (Finsupp.module.{u4, u1, u1} ι R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))))) (Basis.repr.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4) b) (FunLike.coe.{max (succ u5) (succ u2), succ u5, succ u2} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) ι' (fun (_x : ι') => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : ι') => S) _x) (Finsupp.funLike.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u5), succ u3, max (succ u2) (succ u5)} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _x) (SMulHomClass.toFunLike.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribSMul.toSMulZeroClass.{u2, u3} S A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (DistribMulAction.toDistribSMul.{u2, u3} S A (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toZero.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) j)) i)
 Case conversion may be inaccurate. Consider using '#align basis.smul_repr_mk Basis.smul_repr_mkₓ'. -/
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)
     (x i j) : (b.smul c).repr x (i, j) = b.repr (c.repr x j) i :=

93287238

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -56,7 +56,7 @@ variable (R S A B)
 lean 3 declaration is
   forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] (r : R) [_inst_12 : Invertible.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) r)], Invertible.{u3} A (MulOneClass.toHasMul.{u3} A (MulZeroOneClass.toMulOneClass.{u3} A (NonAssocSemiring.toMulZeroOneClass.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (MulOneClass.toHasOne.{u3} A (MulZeroOneClass.toMulOneClass.{u3} A (NonAssocSemiring.toMulZeroOneClass.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) r)
 but is expected to have type
-  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (r : R) [_inst_12 : Invertible.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) r)], Invertible.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3))) (Semiring.toOne.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) r)
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (r : R) [_inst_12 : Invertible.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)))) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) r) _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) r)], Invertible.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3))) (Semiring.toOne.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) _inst_3) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) r)
 Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTowerₓ'. -/
 /-- Suppose that `R -> S -> A` is a tower of algebras.
 If an element `r : R` is invertible in `S`, then it is invertible in `A`. -/
@@ -103,7 +103,7 @@ variable (b : Basis ι R M) (h : Function.Bijective (algebraMap R A))
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))], (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) -> (Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) -> (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)
 but is expected to have type
-  forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))], (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) -> (Function.Bijective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) -> (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)
+  forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u4} A M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u4} A M (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u4} R M (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u4} R M (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3)) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))], (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) -> (Function.Bijective.{succ u1, succ u2} R A (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) -> (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)
 Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs Basis.algebraMapCoeffsₓ'. -/
 /-- If `R` and `A` have a bijective `algebra_map R A` and act identically on `M`,
 then a basis for `M` as `R`-module is also a basis for `M` as `R'`-module. -/
@@ -116,7 +116,7 @@ noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u4} M (coeFn.{max (succ u3) (succ u2) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) (fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u2) (succ u4), succ u3, succ u4} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (fun (_x : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) b i)
 but is expected to have type
-  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u2} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u2} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u2} A M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u1, u2} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b i)
+  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u2} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u2} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u2} A M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u1, u2} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b i)
 Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_applyₓ'. -/
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
@@ -126,7 +126,7 @@ theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u3) (succ u4)} ((fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (coeFn.{max (succ u3) (succ u2) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) (fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u2) (succ u4), succ u3, succ u4} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (fun (_x : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) b)
 but is expected to have type
-  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u1} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u1} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u1} A M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u1} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u1} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u4, u1} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u2) (succ u1)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u2, u1} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b)
+  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u1} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u1} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u1} A M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u1} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u1} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u4, u1} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u2) (succ u1)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u2, u1} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b)
 Case conversion may be inaccurate. Consider using '#align basis.coe_algebra_map_coeffs Basis.coe_algebraMapCoeffsₓ'. -/
 @[simp]
 theorem Basis.coe_algebraMapCoeffs : (b.algebraMapCoeffs A h : ι → M) = b :=
@@ -233,7 +233,7 @@ variable [CommRing R] [Ring S] [Algebra R S]
 lean 3 declaration is
   forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)] {ι : Type.{u3}} [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_5 : Nontrivial.{u2} S], (Basis.{u3, u1, u2} ι R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_3)) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_3)))
 but is expected to have type
-  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2)] {ι : Type.{u1}} [_inst_4 : NoZeroDivisors.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))] [_inst_5 : Nontrivial.{u3} S], (Basis.{u1, u2, u3} ι R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)) -> (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)))
+  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2)] {ι : Type.{u1}} [_inst_4 : NoZeroDivisors.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))] [_inst_5 : Nontrivial.{u3} S], (Basis.{u1, u2, u3} ι R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)) -> (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)))
 Case conversion may be inaccurate. Consider using '#align basis.algebra_map_injective Basis.algebraMap_injectiveₓ'. -/
 theorem Basis.algebraMap_injective {ι : Type _} [NoZeroDivisors R] [Nontrivial S]
     (b : Basis ι R S) : Function.Injective (algebraMap R S) :=

93287238

bump to nightly-2023-03-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

53b827ba

Diff

@@ -116,7 +116,7 @@ noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u4} M (coeFn.{max (succ u3) (succ u2) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) (fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u2) (succ u4), succ u3, succ u4} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (fun (_x : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) b i)
 but is expected to have type
-  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u2} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u2} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u2} A M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) _x) (Basis.funLike.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u1, u2} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) _x) (Basis.funLike.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b i)
+  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u2} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u2} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u2} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u2} A M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u2} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u2} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u4, u2} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u2} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u2} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_3)) (Module.toMulActionWithZero.{u3, u2} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))) (i : ι), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) i) (FunLike.coe.{max (max (succ u4) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u4, u2} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u1, u2} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h) i) (FunLike.coe.{max (max (succ u3) (succ u1)) (succ u2), succ u1, succ u2} (Basis.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u1, u3, u2} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b i)
 Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_applyₓ'. -/
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
@@ -126,7 +126,7 @@ theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :
 lean 3 declaration is
   forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u3) (succ u4)} ((fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (coeFn.{max (succ u3) (succ u2) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) (fun (_x : Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u2) (succ u4), succ u3, succ u4} (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)) (Basis.algebraMapCoeffs.{u1, u2, u3, u4} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (coeFn.{max (succ u3) (succ u1) (succ u4), max (succ u3) (succ u4)} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) (fun (_x : Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) => ι -> M) (FunLike.hasCoeToFun.{max (succ u3) (succ u1) (succ u4), succ u3, succ u4} (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => M) (Basis.funLike.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6)) b)
 but is expected to have type
-  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u1} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u1} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u1} A M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u1} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u1} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u4, u1} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u2) (succ u1)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) a) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) _x) (Basis.funLike.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u2, u1} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.546 : ι) => M) _x) (Basis.funLike.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b)
+  forall {R : Type.{u3}} (A : Type.{u4}) {ι : Type.{u2}} {M : Type.{u1}} [_inst_1 : CommSemiring.{u3} R] [_inst_2 : Semiring.{u4} A] [_inst_3 : AddCommMonoid.{u1} M] [_inst_4 : Algebra.{u3, u4} R A _inst_1 _inst_2] [_inst_5 : Module.{u4, u1} A M _inst_2 _inst_3] [_inst_6 : Module.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u3, u4, u1} R A M (Algebra.toSMul.{u3, u4} R A _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u4, u1} A M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u4, u1} A M (MonoidWithZero.toZero.{u4} A (Semiring.toMonoidWithZero.{u4} A _inst_2)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u4, u1} A M (Semiring.toMonoidWithZero.{u4} A _inst_2) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u4, u1} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u3, u1} R M (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (SMulWithZero.toSMulZeroClass.{u3, u1} R M (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (MulActionWithZero.toSMulWithZero.{u3, u1} R M (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (AddMonoid.toZero.{u1} M (AddCommMonoid.toAddMonoid.{u1} M _inst_3)) (Module.toMulActionWithZero.{u3, u1} R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6))))] (b : Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) (h : Function.Bijective.{succ u3, succ u4} R A (FunLike.coe.{max (succ u3) (succ u4), succ u3, succ u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u4} A (Semiring.toNonAssocSemiring.{u4} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u3 u4, u3, u4} (RingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2) (RingHom.instRingHomClassRingHom.{u3, u4} R A (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)) (Semiring.toNonAssocSemiring.{u4} A _inst_2))))) (algebraMap.{u3, u4} R A _inst_1 _inst_2 _inst_4))), Eq.{max (succ u2) (succ u1)} (forall (a : ι), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) a) (FunLike.coe.{max (max (succ u4) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u4, u1} ι A M _inst_2 _inst_3 _inst_5) (Basis.algebraMapCoeffs.{u3, u4, u2, u1} R A ι M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 b h)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), succ u2, succ u1} (Basis.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) ι (fun (_x : ι) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι) => M) _x) (Basis.funLike.{u2, u3, u1} ι R M (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_6) b)
 Case conversion may be inaccurate. Consider using '#align basis.coe_algebra_map_coeffs Basis.coe_algebraMapCoeffsₓ'. -/
 @[simp]
 theorem Basis.coe_algebraMapCoeffs : (b.algebraMapCoeffs A h : ι → M) = b :=
@@ -175,7 +175,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
 where the `(i, j)`th basis vector is `b i • c j`. -/
 noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) :
     Basis (ι × ι') R A :=
-  Basis.of_repr
+  Basis.ofRepr
     (c.repr.restrictScalars R ≪≫ₗ
       (Finsupp.lcongr (Equiv.refl _) b.repr ≪≫ₗ
         ((finsuppProdLEquiv R).symm ≪≫ₗ

93287238

bump to nightly-2023-03-19-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1f4705ccdfe1e557fc54a0ce081a05e33d2e6240

b19efad4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module ring_theory.algebra_tower
-! leanprover-community/mathlib commit 94825b2b0b982306be14d891c4f063a1eca4f370
+! leanprover-community/mathlib commit 932872382355f00112641d305ba0619305dc8642
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.LinearAlgebra.Basis
 /-!
 # Towers of algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We set up the basic theory of algebra towers.
 An algebra tower A/S/R is expressed by having instances of `algebra A S`,
 `algebra R S`, `algebra R A` and `is_scalar_tower R S A`, the later asserting the

94825b2b

bump to nightly-2023-03-17-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/da3fc4a33ff6bc75f077f691dc94c217b8d41559

4420e8a1

Diff

@@ -49,6 +49,12 @@ variable [IsScalarTower R S A] [IsScalarTower R S B]
 
 variable (R S A B)
 
+/- warning: is_scalar_tower.invertible.algebra_tower -> IsScalarTower.Invertible.algebraTower is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u2, u3} S A (CommSemiring.toSemiring.{u2} S _inst_2) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u2, u3} S A _inst_2 _inst_3 _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (Algebra.toModule.{u1, u3} R A _inst_1 _inst_3 _inst_8)))))] (r : R) [_inst_12 : Invertible.{u2} S (Distrib.toHasMul.{u2} S (NonUnitalNonAssocSemiring.toDistrib.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (AddMonoidWithOne.toOne.{u2} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} S (NonAssocSemiring.toAddCommMonoidWithOne.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) r)], Invertible.{u3} A (MulOneClass.toHasMul.{u3} A (MulZeroOneClass.toMulOneClass.{u3} A (NonAssocSemiring.toMulZeroOneClass.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (MulOneClass.toHasOne.{u3} A (MulZeroOneClass.toMulOneClass.{u3} A (NonAssocSemiring.toMulZeroOneClass.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)))) (coeFn.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (fun (_x : RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) => R -> A) (RingHom.hasCoeToFun.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) r)
+but is expected to have type
+  forall (R : Type.{u1}) (S : Type.{u2}) (A : Type.{u3}) [_inst_1 : CommSemiring.{u1} R] [_inst_2 : CommSemiring.{u2} S] [_inst_3 : Semiring.{u3} A] [_inst_5 : Algebra.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2)] [_inst_6 : Algebra.{u2, u3} S A _inst_2 _inst_3] [_inst_8 : Algebra.{u1, u3} R A _inst_1 _inst_3] [_inst_10 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) (Algebra.toSMul.{u2, u3} S A _inst_2 _inst_3 _inst_6) (Algebra.toSMul.{u1, u3} R A _inst_1 _inst_3 _inst_8)] (r : R) [_inst_12 : Invertible.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonUnitalNonAssocSemiring.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (Semiring.toNonAssocSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)))) (Semiring.toOne.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) (CommSemiring.toSemiring.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) r) _inst_2)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)) (RingHom.instRingHomClassRingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} S (CommSemiring.toSemiring.{u2} S _inst_2)))))) (algebraMap.{u1, u2} R S _inst_1 (CommSemiring.toSemiring.{u2} S _inst_2) _inst_5) r)], Invertible.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (NonUnitalNonAssocSemiring.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Semiring.toNonAssocSemiring.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3))) (Semiring.toOne.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) _inst_3) (FunLike.coe.{max (succ u1) (succ u3), succ u1, succ u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_3)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u3, u1, u3} (RingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3) (RingHom.instRingHomClassRingHom.{u1, u3} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u3} A _inst_3))))) (algebraMap.{u1, u3} R A _inst_1 _inst_3 _inst_8) r)
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTowerₓ'. -/
 /-- Suppose that `R -> S -> A` is a tower of algebras.
 If an element `r : R` is invertible in `S`, then it is invertible in `A`. -/
 def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
@@ -57,6 +63,12 @@ def Invertible.algebraTower (r : R) [Invertible (algebraMap R S r)] :
     (IsScalarTower.algebraMap_apply R S A r)
 #align is_scalar_tower.invertible.algebra_tower IsScalarTower.Invertible.algebraTower
 
+/- warning: is_scalar_tower.invertible_algebra_coe_nat -> IsScalarTower.invertibleAlgebraCoeNat is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_3 : Semiring.{u2} A] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_3] (n : Nat) [inv : Invertible.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddMonoidWithOne.toOne.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Nat R (HasLiftT.mk.{1, succ u1} Nat R (CoeTCₓ.coe.{1, succ u1} Nat R (Nat.castCoe.{u1} R (AddMonoidWithOne.toNatCast.{u1} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u1} R (NonAssocSemiring.toAddCommMonoidWithOne.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))))) n)], Invertible.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3)))) ((fun (a : Type) (b : Type.{u2}) [self : HasLiftT.{1, succ u2} a b] => self.0) Nat A (HasLiftT.mk.{1, succ u2} Nat A (CoeTCₓ.coe.{1, succ u2} Nat A (Nat.castCoe.{u2} A (AddMonoidWithOne.toNatCast.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))))))) n)
+but is expected to have type
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommSemiring.{u1} R] [_inst_3 : Semiring.{u2} A] [_inst_8 : Algebra.{u1, u2} R A _inst_1 _inst_3] (n : Nat) [inv : Invertible.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toOne.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Nat.cast.{u1} R (Semiring.toNatCast.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) n)], Invertible.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_3))) (Semiring.toOne.{u2} A _inst_3) (Nat.cast.{u2} A (Semiring.toNatCast.{u2} A _inst_3) n)
+Case conversion may be inaccurate. Consider using '#align is_scalar_tower.invertible_algebra_coe_nat IsScalarTower.invertibleAlgebraCoeNatₓ'. -/
 /-- A natural number that is invertible when coerced to `R` is also invertible
 when coerced to any `R`-algebra. -/
 def invertibleAlgebraCoeNat (n : ℕ) [inv : Invertible (n : R)] : Invertible (n : A) :=
@@ -84,6 +96,12 @@ variable [Algebra R A] [Module A M] [Module R M] [IsScalarTower R A M]
 
 variable (b : Basis ι R M) (h : Function.Bijective (algebraMap R A))
 
+/- warning: basis.algebra_map_coeffs -> Basis.algebraMapCoeffs is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} (A : Type.{u2}) {ι : Type.{u3}} {M : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : AddCommMonoid.{u4} M] [_inst_4 : Algebra.{u1, u2} R A _inst_1 _inst_2] [_inst_5 : Module.{u2, u4} A M _inst_2 _inst_3] [_inst_6 : Module.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u4} R A M (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u4} A M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u4} A M (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u4} A M (Semiring.toMonoidWithZero.{u2} A _inst_2) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u2, u4} A M _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u4} R M (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u4} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u4} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u4} M (AddMonoid.toAddZeroClass.{u4} M (AddCommMonoid.toAddMonoid.{u4} M _inst_3))) (Module.toMulActionWithZero.{u1, u4} R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))], (Basis.{u3, u1, u4} ι R M (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6) -> (Function.Bijective.{succ u1, succ u2} R A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_4))) -> (Basis.{u3, u2, u4} ι A M _inst_2 _inst_3 _inst_5)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs Basis.algebraMapCoeffsₓ'. -/
 /-- If `R` and `A` have a bijective `algebra_map R A` and act identically on `M`,
 then a basis for `M` as `R`-module is also a basis for `M` as `R'`-module. -/
 @[simps]
@@ -91,10 +109,22 @@ noncomputable def Basis.algebraMapCoeffs : Basis ι A M :=
   b.mapCoeffs (RingEquiv.ofBijective _ h) fun c x => by simp
 #align basis.algebra_map_coeffs Basis.algebraMapCoeffs
 
+/- warning: basis.algebra_map_coeffs_apply -> Basis.algebraMapCoeffs_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_applyₓ'. -/
 theorem Basis.algebraMapCoeffs_apply (i : ι) : b.algebraMapCoeffs A h i = b i :=
   b.mapCoeffs_apply _ _ _
 #align basis.algebra_map_coeffs_apply Basis.algebraMapCoeffs_apply
 
+/- warning: basis.coe_algebra_map_coeffs -> Basis.coe_algebraMapCoeffs is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.coe_algebra_map_coeffs Basis.coe_algebraMapCoeffsₓ'. -/
 @[simp]
 theorem Basis.coe_algebraMapCoeffs : (b.algebraMapCoeffs A h : ι → M) = b :=
   b.coe_mapCoeffs _ _
@@ -117,6 +147,7 @@ variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
 variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print linearIndependent_smul /-
 theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁} {c : ι' → A}
     (hb : LinearIndependent R b) (hc : LinearIndependent S c) :
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 :=
@@ -134,7 +165,9 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     exact hb _ _ (hc _ _ h1 k (Finset.mem_image_of_mem _ hik)) i (Finset.mem_image_of_mem _ hik)
   exact hg _ hik
 #align linear_independent_smul linearIndependent_smul
+-/
 
+#print Basis.smul /-
 /-- `basis.smul (b : basis ι R S) (c : basis ι S A)` is the `R`-basis on `A`
 where the `(i, j)`th basis vector is `b i • c j`. -/
 noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) :
@@ -145,17 +178,31 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
         ((finsuppProdLEquiv R).symm ≪≫ₗ
           Finsupp.lcongr (Equiv.prodComm ι' ι) (LinearEquiv.refl _ _))))
 #align basis.smul Basis.smul
+-/
 
+/- warning: basis.smul_repr -> Basis.smul_repr is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (ij : Prod.{u4, u5} ι ι'), Eq.{succ u1} R (coeFn.{max (succ (max u4 u5)) (succ u1), max (succ (max u4 u5)) (succ u1)} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (fun (_x : Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) => (Prod.{u4, u5} ι ι') -> R) (Finsupp.coeFun.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (coeFn.{max (succ u3) (succ (max (max u4 u5) u1)), max (succ u3) (succ (max (max u4 u5) u1))} (LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (fun (_x : LinearEquiv.{u1, u1, u3, max (max u4 u5) u1} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} 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(RingHomInvPair.ids.{u2} S _inst_2)) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (ij : Prod.{u4, u5} ι ι'), Eq.{succ u1} ((fun 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) (Prod.snd.{u4, u5} ι ι' ij))) (Prod.fst.{u4, u5} ι ι' ij))
+Case conversion may be inaccurate. Consider using '#align basis.smul_repr Basis.smul_reprₓ'. -/
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
     (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]
 #align basis.smul_repr Basis.smul_repr
 
+/- warning: basis.smul_repr_mk -> Basis.smul_repr_mk is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (SMulZeroClass.toHasSmul.{u1, u2} R S (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R S (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R S (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} S (AddMonoid.toAddZeroClass.{u2} S (AddCommMonoid.toAddMonoid.{u2} S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4))))) (SMulZeroClass.toHasSmul.{u2, u3} S A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u2, u3} S A (MulZeroClass.toHasZero.{u2} S (MulZeroOneClass.toMulZeroClass.{u2} S (MonoidWithZero.toMulZeroOneClass.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u3} R A (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (SMulWithZero.toSmulZeroClass.{u1, u3} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u3} A (AddMonoid.toAddZeroClass.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3))) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} R (coeFn.{max (succ (max u4 u5)) (succ u1), max (succ (max u4 u5)) (succ u1)} (Finsupp.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R 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+but is expected to have type
+  forall {R : Type.{u1}} {S : Type.{u2}} {A : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} S] [_inst_3 : AddCommMonoid.{u3} A] [_inst_4 : Algebra.{u1, u2} R S _inst_1 _inst_2] [_inst_5 : Module.{u2, u3} S A _inst_2 _inst_3] [_inst_6 : Module.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_7 : IsScalarTower.{u1, u2, u3} R S A (Algebra.toSMul.{u1, u2} R S _inst_1 _inst_2 _inst_4) (SMulZeroClass.toSMul.{u2, u3} S A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u2, u3} S A (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u2, u3} S A (Semiring.toMonoidWithZero.{u2} S _inst_2) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u2, u3} S A _inst_2 _inst_3 _inst_5)))) (SMulZeroClass.toSMul.{u1, u3} R A (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (SMulWithZero.toSMulZeroClass.{u1, u3} R A (CommMonoidWithZero.toZero.{u1} R (CommSemiring.toCommMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (MulActionWithZero.toSMulWithZero.{u1, u3} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddMonoid.toZero.{u3} A (AddCommMonoid.toAddMonoid.{u3} A _inst_3)) (Module.toMulActionWithZero.{u1, u3} R A (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_6))))] {ι : Type.{u4}} {ι' : Type.{u5}} (b : Basis.{u4, u1, u2} ι R S (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Algebra.toModule.{u1, u2} R S _inst_1 _inst_2 _inst_4)) (c : Basis.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5) (x : A) (i : ι) (j : ι'), Eq.{succ u1} ((fun 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(NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 (Finsupp.addCommMonoid.{max u4 u5, u1} (Prod.{u4, u5} ι ι') R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) _inst_6 (Finsupp.module.{max u4 u5, u1, u1} (Prod.{u4, u5} ι ι') R R (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u3, max (max u1 u4) u5, max (max 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(MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribSMul.toSMulZeroClass.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddMonoid.toAddZeroClass.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))))) (DistribMulAction.toDistribSMul.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u2 u3) u5, u2, u3, max u2 u5} (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (MonoidWithZero.toMonoid.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2)) (AddCommMonoid.toAddMonoid.{u3} A _inst_3) (AddCommMonoid.toAddMonoid.{max u2 u5} (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))))) (Module.toDistribMulAction.{u2, u3} S A _inst_2 _inst_3 _inst_5) (Module.toDistribMulAction.{u2, max u2 u5} S (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) (SemilinearMapClass.distribMulActionHomClass.{u2, u3, max u2 u5, max (max u2 u3) u5} S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (SemilinearEquivClass.instSemilinearMapClass.{u2, u2, u3, max u2 u5, max (max u2 u3) u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) (LinearEquiv.{u2, u2, u3, max u2 u5} S S _inst_2 _inst_2 (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u2, u2, u3, max u2 u5} S S A (Finsupp.{u5, u2} ι' S (MonoidWithZero.toZero.{u2} S (Semiring.toMonoidWithZero.{u2} S _inst_2))) _inst_2 _inst_2 _inst_3 (Finsupp.addCommMonoid.{u5, u2} ι' S (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)))) _inst_5 (Finsupp.module.{u5, u2, u2} ι' S S _inst_2 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2))) (Semiring.toModule.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHom.id.{u2} S (Semiring.toNonAssocSemiring.{u2} S _inst_2)) (RingHomInvPair.ids.{u2} S _inst_2) (RingHomInvPair.ids.{u2} S _inst_2)))))) (Basis.repr.{u5, u2, u3} ι' S A _inst_2 _inst_3 _inst_5 c) x) j)) i)
+Case conversion may be inaccurate. Consider using '#align basis.smul_repr_mk Basis.smul_repr_mkₓ'. -/
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)
     (x i j) : (b.smul c).repr x (i, j) = b.repr (c.repr x j) i :=
   b.smul_repr c x (i, j)
 #align basis.smul_repr_mk Basis.smul_repr_mk
 
+#print Basis.smul_apply /-
 @[simp]
 theorem Basis.smul_apply {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (ij) :
     (b.smul c) ij = b ij.1 • c ij.2 := by
@@ -169,6 +216,7 @@ theorem Basis.smul_apply {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (
   · simp [hi, Finsupp.single_apply]
   · simp [hi]
 #align basis.smul_apply Basis.smul_apply
+-/
 
 end Semiring
 
@@ -178,6 +226,12 @@ variable {R S}
 
 variable [CommRing R] [Ring S] [Algebra R S]
 
+/- warning: basis.algebra_map_injective -> Basis.algebraMap_injective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {S : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Ring.{u2} S] [_inst_3 : Algebra.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2)] {ι : Type.{u3}} [_inst_4 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (Ring.toDistrib.{u1} R (CommRing.toRing.{u1} R _inst_1))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R _inst_1))))))] [_inst_5 : Nontrivial.{u2} S], (Basis.{u3, u1, u2} ι R S (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} S (NonUnitalNonAssocRing.toAddCommGroup.{u2} S (NonAssocRing.toNonUnitalNonAssocRing.{u2} S (Ring.toNonAssocRing.{u2} S _inst_2)))) (Algebra.toModule.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_3)) -> (Function.Injective.{succ u1, succ u2} R S (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (fun (_x : RingHom.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) => R -> S) (RingHom.hasCoeToFun.{u1, u2} R S (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u2} S (Ring.toSemiring.{u2} S _inst_2))) (algebraMap.{u1, u2} R S (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} S _inst_2) _inst_3)))
+but is expected to have type
+  forall {R : Type.{u2}} {S : Type.{u3}} [_inst_1 : CommRing.{u2} R] [_inst_2 : Ring.{u3} S] [_inst_3 : Algebra.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2)] {ι : Type.{u1}} [_inst_4 : NoZeroDivisors.{u2} R (NonUnitalNonAssocRing.toMul.{u2} R (NonAssocRing.toNonUnitalNonAssocRing.{u2} R (Ring.toNonAssocRing.{u2} R (CommRing.toRing.{u2} R _inst_1)))) (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))] [_inst_5 : Nontrivial.{u3} S], (Basis.{u1, u2, u3} ι R S (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (Algebra.toModule.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)) -> (Function.Injective.{succ u2, succ u3} R S (FunLike.coe.{max (succ u2) (succ u3), succ u2, succ u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => S) _x) (MulHomClass.toFunLike.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u3} S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} S (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u3, u2, u3} (RingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2))) R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u3} R S (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_1))) (Semiring.toNonAssocSemiring.{u3} S (Ring.toSemiring.{u3} S _inst_2)))))) (algebraMap.{u2, u3} R S (CommRing.toCommSemiring.{u2} R _inst_1) (Ring.toSemiring.{u3} S _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align basis.algebra_map_injective Basis.algebraMap_injectiveₓ'. -/
 theorem Basis.algebraMap_injective {ι : Type _} [NoZeroDivisors R] [Nontrivial S]
     (b : Basis ι R S) : Function.Injective (algebraMap R S) :=
   have : NoZeroSMulDivisors R S := b.NoZeroSMulDivisors
@@ -193,18 +247,23 @@ variable {A} {C D : Type _} [CommSemiring A] [CommSemiring C] [CommSemiring D] [
 
 variable (f : C →ₐ[A] D) (B) [CommSemiring B] [Algebra A B] [Algebra B C] [IsScalarTower A B C]
 
+#print AlgHom.restrictDomain /-
 /-- Restrict the domain of an `alg_hom`. -/
 def AlgHom.restrictDomain : B →ₐ[A] D :=
   f.comp (IsScalarTower.toAlgHom A B C)
 #align alg_hom.restrict_domain AlgHom.restrictDomain
+-/
 
+#print AlgHom.extendScalars /-
 /-- Extend the scalars of an `alg_hom`. -/
 def AlgHom.extendScalars : @AlgHom B C D _ _ _ _ (f.restrictDomain B).toRingHom.toAlgebra :=
   { f with commutes' := fun _ => rfl }
 #align alg_hom.extend_scalars AlgHom.extendScalars
+-/
 
 variable {B}
 
+#print algHomEquivSigma /-
 /-- `alg_hom`s from the top of a tower are equivalent to a pair of `alg_hom`s. -/
 def algHomEquivSigma : (C →ₐ[A] D) ≃ Σf : B →ₐ[A] D, @AlgHom B C D _ _ _ _ f.toRingHom.toAlgebra
     where
@@ -224,6 +283,7 @@ def algHomEquivSigma : (C →ₐ[A] D) ≃ Σf : B →ₐ[A] D, @AlgHom B C D _
       exact (hg x).symm
     rfl
 #align alg_hom_equiv_sigma algHomEquivSigma
+-/
 
 end AlgHomTower

94825b2b

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

94825b2b

chore: tidy various files (#11624)

483848e8

Diff

@@ -149,8 +149,7 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
     (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by
-  set_option tactic.skipAssignedInstances false in
-  simp [Basis.smul]; rfl
+  simp [Basis.smul]
 #align basis.smul_repr Basis.smul_repr
 
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)

94825b2b

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -38,9 +38,7 @@ namespace IsScalarTower
 section Semiring
 
 variable [CommSemiring R] [CommSemiring S] [Semiring A] [Semiring B]
-
 variable [Algebra R S] [Algebra S A] [Algebra S B] [Algebra R A] [Algebra R B]
-
 variable [IsScalarTower R S A] [IsScalarTower R S B]
 
 
@@ -64,7 +62,6 @@ end Semiring
 section CommSemiring
 
 variable [CommSemiring R] [CommSemiring A] [CommSemiring B]
-
 variable [Algebra R A] [Algebra A B] [Algebra R B] [IsScalarTower R A B]
 
 end CommSemiring
@@ -74,9 +71,7 @@ end IsScalarTower
 section AlgebraMapCoeffs
 
 variable {R} {ι M : Type*} [CommSemiring R] [Semiring A] [AddCommMonoid M]
-
 variable [Algebra R A] [Module A M] [Module R M] [IsScalarTower R A M]
-
 variable (b : Basis ι R M) (h : Function.Bijective (algebraMap R A))
 
 /-- If `R` and `A` have a bijective `algebraMap R A` and act identically on `M`,
@@ -108,9 +103,7 @@ open BigOperators
 universe v₁ w₁
 
 variable {R S A}
-
 variable [Semiring R] [Semiring S] [AddCommMonoid A]
-
 variable [Module R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁} {c : ι' → A}
@@ -184,7 +177,6 @@ end Semiring
 section Ring
 
 variable {R S}
-
 variable [CommRing R] [Ring S] [Algebra R S]
 
 -- Porting note: Needed to add Algebra.toModule below

94825b2b

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -102,7 +102,8 @@ section Semiring
 
 open Finsupp
 
-open BigOperators Classical
+open scoped Classical
+open BigOperators
 
 universe v₁ w₁

94825b2b

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -154,7 +154,9 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
-    (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]; rfl
+    (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by
+  set_option tactic.skipAssignedInstances false in
+  simp [Basis.smul]; rfl
 #align basis.smul_repr Basis.smul_repr
 
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)

94825b2b

feat(Algebra): generalize Basis.smul (#9382)

Add various LinearMap.CompatibleSMul instances that ultimately lead to generalization of Basis.smul to allow a noncommutative base ring. The key observations that allows the generalization are IsScalarTower.smulHomClass and isScalarTower_of_injective.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

63e722e8

Diff

@@ -108,9 +108,9 @@ universe v₁ w₁
 
 variable {R S A}
 
-variable [CommSemiring R] [Semiring S] [AddCommMonoid A]
+variable [Semiring R] [Semiring S] [AddCommMonoid A]
 
-variable [Algebra R S] [Module S A] [Module R A] [IsScalarTower R S A]
+variable [Module R S] [Module S A] [Module R A] [IsScalarTower R S A]
 
 theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁} {c : ι' → A}
     (hb : LinearIndependent R b) (hc : LinearIndependent S c) :
@@ -128,10 +128,23 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
   exact hg _ hik
 #align linear_independent_smul linearIndependent_smul
 
+variable (R)
+
+-- LinearIndependent is enough if S is a ring rather than semiring.
+theorem Basis.isScalarTower_of_nonempty {ι} [Nonempty ι] (b : Basis ι S A) : IsScalarTower R S S :=
+  (b.repr.symm.comp <| lsingle <| Classical.arbitrary ι).isScalarTower_of_injective R
+    (b.repr.symm.injective.comp <| single_injective _)
+
+theorem Basis.isScalarTower_finsupp {ι} (b : Basis ι S A) : IsScalarTower R S (ι →₀ S) :=
+  b.repr.symm.isScalarTower_of_injective R b.repr.symm.injective
+
+variable {R}
+
 /-- `Basis.SMul (b : Basis ι R S) (c : Basis ι S A)` is the `R`-basis on `A`
 where the `(i, j)`th basis vector is `b i • c j`. -/
 noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) :
     Basis (ι × ι') R A :=
+  haveI := c.isScalarTower_finsupp R
   .ofRepr
     (c.repr.restrictScalars R ≪≫ₗ
       (Finsupp.lcongr (Equiv.refl _) b.repr ≪≫ₗ
@@ -141,7 +154,7 @@ noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R
 
 @[simp]
 theorem Basis.smul_repr {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) (x ij) :
-    (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]
+    (b.smul c).repr x ij = b.repr (c.repr x ij.2) ij.1 := by simp [Basis.smul]; rfl
 #align basis.smul_repr Basis.smul_repr
 
 theorem Basis.smul_repr_mk {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A)

94825b2b

chore: split Mathlib.Algebra.Invertible (#6973)

Mathlib.Algebra.Invertible is used by fundamental tactics, and this essentially splits it into the part used by NormNum, and everything else.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d67f31e1

Diff

@@ -4,7 +4,6 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
 import Mathlib.Algebra.Algebra.Tower
-import Mathlib.Algebra.Invertible
 import Mathlib.Algebra.Module.BigOperators
 import Mathlib.LinearAlgebra.Basis

94825b2b

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -74,7 +74,7 @@ end IsScalarTower
 
 section AlgebraMapCoeffs
 
-variable {R} {ι M : Type _} [CommSemiring R] [Semiring A] [AddCommMonoid M]
+variable {R} {ι M : Type*} [CommSemiring R] [Semiring A] [AddCommMonoid M]
 
 variable [Algebra R A] [Module A M] [Module R M] [IsScalarTower R A M]
 
@@ -173,7 +173,7 @@ variable {R S}
 variable [CommRing R] [Ring S] [Algebra R S]
 
 -- Porting note: Needed to add Algebra.toModule below
-theorem Basis.algebraMap_injective {ι : Type _} [NoZeroDivisors R] [Nontrivial S]
+theorem Basis.algebraMap_injective {ι : Type*} [NoZeroDivisors R] [Nontrivial S]
     (b : @Basis ι R S _ _ Algebra.toModule) : Function.Injective (algebraMap R S) :=
   have : NoZeroSMulDivisors R S := b.noZeroSMulDivisors
   NoZeroSMulDivisors.algebraMap_injective R S
@@ -183,7 +183,7 @@ end Ring
 
 section AlgHomTower
 
-variable {A} {C D : Type _} [CommSemiring A] [CommSemiring C] [CommSemiring D] [Algebra A C]
+variable {A} {C D : Type*} [CommSemiring A] [CommSemiring C] [CommSemiring D] [Algebra A C]
   [Algebra A D]
 
 variable (f : C →ₐ[A] D) [CommSemiring B] [Algebra A B] [Algebra B C] [IsScalarTower A B C]

94825b2b

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module ring_theory.algebra_tower
-! leanprover-community/mathlib commit 94825b2b0b982306be14d891c4f063a1eca4f370
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Tower
 import Mathlib.Algebra.Invertible
 import Mathlib.Algebra.Module.BigOperators
 import Mathlib.LinearAlgebra.Basis
 
+#align_import ring_theory.algebra_tower from "leanprover-community/mathlib"@"94825b2b0b982306be14d891c4f063a1eca4f370"
+
 /-!
 # Towers of algebras

94825b2b

chore: fix grammar in docs (#5668)

15cdb8ec

Diff

@@ -25,7 +25,7 @@ In `FieldTheory/Tower.lean` we use this to prove the tower law for finite extens
 that if `R` and `S` are both fields, then `[A:R] = [A:S] [S:A]`.
 
 In this file we prepare the main lemma:
-if `{bi | i ∈ I}` is an `R`-basis of `S` and `{cj | j ∈ J}` is a `S`-basis
+if `{bi | i ∈ I}` is an `R`-basis of `S` and `{cj | j ∈ J}` is an `S`-basis
 of `A`, then `{bi cj | i ∈ I, j ∈ J}` is an `R`-basis of `A`. This statement does not require the
 base rings to be a field, so we also generalize the lemma to rings in this file.
 -/

94825b2b

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -121,7 +121,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 := by
   rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
-  · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
+  · have h1 : ∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2 = 0 := by
       rw [← hsg]
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>

94825b2b

refactor: use the typeclass SProd to implement overloaded notation · ×ˢ · (#4200)

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

6c01dc6e

Diff

@@ -121,7 +121,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 := by
   rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
-  · have h1 : (∑ i in s.image Prod.fst ×ᶠ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
+  · have h1 : (∑ i in s.image Prod.fst ×ˢ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
       rw [← hsg]
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>

94825b2b

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -121,8 +121,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
     LinearIndependent R fun p : ι × ι' => b p.1 • c p.2 := by
   rw [linearIndependent_iff'] at hb hc; rw [linearIndependent_iff'']; rintro s g hg hsg ⟨i, k⟩
   by_cases hik : (i, k) ∈ s
-  · have h1 : (∑ i in s.image Prod.fst ×ᶠ s.image Prod.snd, g i • b i.1 • c i.2) = 0 :=
-      by
+  · have h1 : (∑ i in s.image Prod.fst ×ᶠ s.image Prod.snd, g i • b i.1 • c i.2) = 0 := by
       rw [← hsg]
       exact
         (Finset.sum_subset Finset.subset_product fun p _ hp =>
@@ -232,8 +231,7 @@ def algHomEquivSigma : (C →ₐ[A] D) ≃ Σf : B →ₐ[A] D, @AlgHom B C D _
     rfl
   right_inv := by
     rintro ⟨⟨⟨⟨⟨f, _⟩, _⟩, _⟩, _⟩, ⟨⟨⟨⟨g, _⟩, _⟩, _⟩, hg⟩⟩
-    obtain rfl : f = fun x => g (algebraMap B C x) :=
-      by
+    obtain rfl : f = fun x => g (algebraMap B C x) := by
       ext x
       exact (hg x).symm
     rfl

94825b2b

chore: fix docs, golf, rename (#3010)

Run fix-comments on Mathlib/LinearAlgebra/Basis.lean.
Rename Basis.of_repr to Basis.ofRepr.
Reflow/minor golf.

4a6b502d

Diff

@@ -137,7 +137,7 @@ theorem linearIndependent_smul {ι : Type v₁} {b : ι → S} {ι' : Type w₁}
 where the `(i, j)`th basis vector is `b i • c j`. -/
 noncomputable def Basis.smul {ι : Type v₁} {ι' : Type w₁} (b : Basis ι R S) (c : Basis ι' S A) :
     Basis (ι × ι') R A :=
-  Basis.of_repr
+  .ofRepr
     (c.repr.restrictScalars R ≪≫ₗ
       (Finsupp.lcongr (Equiv.refl _) b.repr ≪≫ₗ
         ((finsuppProdLEquiv R).symm ≪≫ₗ

94825b2b

feat: port RingTheory.AlgebraTower (#2586)

simps is generating a lemma that the simpNF linter is having an issue again. Guess manual replacement of this lemma is the way to go, bit too sleepy to do that now though. Feel free to jump in!

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

fede9482

`ring_theory.algebra_tower` ⟷ `Mathlib.RingTheory.AlgebraTower`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 423

ring_theory.algebra_tower ⟷ Mathlib.RingTheory.AlgebraTower

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 423

`ring_theory.algebra_tower` ⟷ `Mathlib.RingTheory.AlgebraTower`